Abstract
Abstract Purpose The relationship between root tensile strengths and diameters is often fitted using power law curves. More accurate fitting methodologies were developed, investigating a) the validity of least-squares regression assumptions underlying existing methods, b) how to best quantify intra-diameter variation, and c) whether to fit in terms of tensile strength or tensile force at failure. Methods Regression and maximum likelihood estimation were used to fit various power law models. 6461 tensile strength measurements from 153 existing datasets, covering 103 different plant species, were used to compare models. Results The intra-diameter variation in root strength is proportional to the average strength at each diameter, and is best described using a gamma distribution. When using linear regression on log-transformed measurements, a mathematical correction must be used to avoid underestimating the actual strength (18% on average). Compared to fitting tensile strengths, fitting in terms of root forces at failure was less reliable; the extra emphasis this method places on the effect of large diameters roots was not appropriate because of the typical abundance of thin roots in the field relative to those tested in tension. Average power law fits were proposed for broadleaved trees, conifers, shrubs, grasses and forbs. Conclusion Power law curves should be fitted in terms of root strength rather than root forces at failure, using the newly developed fitting methods that simultaneously fit both the inter-diameter (power law) and intra-diameter variation and can account for fitting bias. This will increase the reliability of future root reinforcement predictions.
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Claims 5
Claim · model-written summary
Intra-diameter variation in root strength is proportional to the average strength at each diameter and is best described by a gamma distribution.
Verbatim
e1“6461 tensile strength measurements from 153 existing datasets, covering 103 different plant species, were used to compare models”
e2“The intra-diameter variation in root strength is proportional to the average strength at each diameter, and is best described using a gamma distribution”
Claim · model-written summary
Linear regression on log-transformed root strength measurements underestimates actual strength by 18% on average without a correction.
Verbatim
e1“6461 tensile strength measurements from 153 existing datasets, covering 103 different plant species, were used to compare models”
e3“When using linear regression on log-transformed measurements, a mathematical correction must be used to avoid underestimating the actual strength (18% on average)”
Claim · model-written summary
Fitting in terms of root forces at failure was less reliable than fitting tensile strengths.
Verbatim
e1“6461 tensile strength measurements from 153 existing datasets, covering 103 different plant species, were used to compare models”
e4“Compared to fitting tensile strengths, fitting in terms of root forces at failure was less reliable”
Claim · model-written summary
Average power law fits were proposed for broadleaved trees, conifers, shrubs, grasses and forbs.
Verbatim
e5“Average power law fits were proposed for broadleaved trees, conifers, shrubs, grasses and forbs”
Claim · model-written summary
Power law curves should be fitted in terms of root strength rather than root forces at failure.
Verbatim
e1“6461 tensile strength measurements from 153 existing datasets, covering 103 different plant species, were used to compare models”
e6“Power law curves should be fitted in terms of root strength rather than root forces at failure”